tprak

commit 825403318ee7db3d58af231dfde6a5a27f9bd52a
Author: miksa234 <milutin@popovic.xyz>
Date:   Tue,  6 Apr 2021 18:23:29 +0200

started theoretical physics praktikum done small exercise 4.3'

Diffstat:
A
.ipynb_checkpoints/Untitled-checkpoint.ipynb
 | 
6
++++++
A
tp43.py
 | 
32
++++++++++++++++++++++++++++++++

2 files changed, 38 insertions(+), 0 deletions(-)
diff --git a/.ipynb_checkpoints/Untitled-checkpoint.ipynb b/.ipynb_checkpoints/Untitled-checkpoint.ipynb
@@ -0,0 +1,6 @@
+{
+ "cells": [],
+ "metadata": {},
+ "nbformat": 4,
+ "nbformat_minor": 5
+}
diff --git a/tp43.py b/tp43.py
@@ -0,0 +1,32 @@
+#!/usr/bin/env python3.9
+
+from sympy import *
+
+def main():
+    p_, n, nprime = symbols('p_, n, nprime')
+    vr = Matrix([p_, n, nprime]) # array of variables
+
+    p = Matrix([1, 0.8, 1.2])       # initial guess
+    y = Matrix([0.8, 1.2, 1, 1])    # observables
+    P = eye(4)*25                   # inverse convariace matrix
+    f = Matrix(([n*p_, nprime*p_, n, nprime])) # parameters
+
+
+    for _ in range(10):
+
+        f0 = f.subs({p_:p[0], n:p[1], nprime:p[2]})
+        I0 = y - f0
+
+        # design matrix
+        A = f.jacobian(vr).subs({p_:p[0], n:p[1], nprime:p[2]})
+
+        dp=(A.T @ P @ A).inv() @ A.T @ P @ I0
+
+        p = p + dp
+
+    cov = (A.T @ P @ A).inv()
+    for i in range(3):
+        print(f'{vr[i]}:\t {p[i]}\t\\pm {sqrt(cov[i, i])}')
+
+if __name__ == "__main__":
+    main()